is the root-mean-square (RMS) fluid velocity [1]}, [2]}, [3]}.
The term \(H_*\tau _{\rm sw}\)  is to account for the suppression effect of the phase transition duration for the GW amplitude of the sound wave source. The \(\kappa _\nu \)  factor is the fraction of the latent heat transferred into the kinetic energy of plasma, which is given by the hydrodynamic analysis [4]}.
The peak frequency of the sound wave locates at [1]}
\(f_{\rm sw}=1.9 \times 10^{-5} \frac{\beta }{H} \frac{1}{v_b} \frac{T_*}{100}\left({\frac{g_*}{100}}\right)^{\frac{1}{6}} {\rm Hz }\;.\) 
